Over the years, a number of philosophers and scientists have proposed specific brain mechanisms that could provide the unpredictability expected of "Freedom."

Most of these thinkers made the error of assuming that chance could be the direct cause of our free actions.

And many of them imagined mechanisms that were so close to perfect balance that an infinitesimal amount of energy could make them go this way or that way. Inspired by the ancient liberum arbitrium indifferentiae, they wanted the mental effort involved to be nil, because the very idea of a mental substance affecting the material body was considered a problem.

In English and Romance languages, the term used to describe the decision process, deliberation, is normally assumed to be derived from the Latin verb delibrare, to balance (from libra, scale). This fits with the simple idea that judgments are always balancing two options.

But it is more likely that the options we face are extremely different in many ways that make them hard to evaluate. Moralists have complained that difficult choices are not properly characterized as "indifferent" decisions, nearly in balance.

And it is still more likely that we are always facing not two but multiple alternate possibilities. Our alternative etymology would be to derive deliberation from Latin deliberare, based on liberare, to liberate or set free.

Here are some of the mechanisms suggested to underlie the free will.

• James Clerk Maxwell's "Singularities" (1856)
• Arthur Stanley Eddington's "Free Electrons" (1928)
• Arthur Holly Compton's Photocell Amplifier (1931)
• John Eccles' "Critically Poised Neurons" (1953)
• A. O. Gomes' Quantum Composer (1964)
• Daniel Dennett's Pseudo-random Number Generator (1978)
• Robert Kane's Spinning Wheel of Fortune (1985)
• Laura Waddell Ekstrom's "" (1995?)
• Alfred Mele's Roulette Wheel (1999?)

Maxwell looked for free will in physical conditions that were poised on a knife edge of going this way or that way and which the mind could push in either direction with minimal (ideally zero) energy required. Note that Maxwell anticipates the theory of modern deterministic "chaos" in which infinitesimal differences lead to massive global changes. This is a characteristic of most "amplifier" theories that hope to move microscopic indeterminism to have macroscopic effects.

When the state of things is such that an infinitely small variation of the present state will alter only by an infinitely small quantity the state at some future time, the condition of the system, whether at rest or in motion, is said to be stable; but when an infinitely small variation in the present state may bring about a finite difference in the state of the system in a finite time, the condition of the system is said to be unstable.

It is manifest that the existence of unstable conditions renders impossible the prediction of future events, if our knowledge of the present state is only approximate, and not accurate.

It has been well pointed out by Professor Balfour Stewart that physical stability is the characteristic of those systems from the contemplation of which determinists draw their arguments, and physical instability that of those living bodies, and moral instability that of those developable souls, which furnish to consciousness the conviction of free will.

Having thus pointed out some of the relations of physical science to the question, we are the better prepared to inquire what is meant by determination and what by free will.

No one, I suppose, would assign to free will a more than infinitesimal range. No leopard can change his spots, nor can any one by merely wishing it, or, as some say, willing it, introduce discontinuity into his course of existence. Our free will at the best is like that of Lucretius's atoms — which at quite uncertain times and places deviate in an uncertain manner from their course. In the course of this our mortal life we more or less frequently find ourselves on a physical or moral watershed, where an imperceptible deviation is sufficient to determine into which of two valleys we shall descend. The doctrine of free will asserts that in some such cases the Ego alone is the determining cause. The doctrine of Determinism asserts that in every case. without exception, the result is determined by the previous conditions of the subject, whether bodily or mental, and that Ego is mistaken in supposing himself in any way the cause of the actual result, as both what he is pleased to call decisions and the resultant action are corresponding events due to the same fixed laws.

(Essay on Science and Free Will, 1873)

Six years later, Maxwell was intrigued by the work of three Frenchmen, Boussinesq, Cournot, and St Venant, on singular points in the solution of hydrodynamic equations which suggested complete unpredictability of future states. These resembled Lucretius' (really Epicurus') atomic swerves, and they anticipate modern non-linear, deterministic chaos. Although Maxwell did not find the idea really satisfactory, it did challenge the metaphysics of strict causal determinism.

Maxwell wrote in a letter to Francis Galton² (who never responded to the suggestion):

There are certain cases in which a material system, when it comes to a phase in which the particular path which it is describing coincides with the envelope of all such paths may either continue in the particular path or take to the envelope (which in these cases is also a possible path) and which course it takes is not determined by the forces of the system (which are the same for both cases) but when the bifurcation of path occurs, the system, ipso facto, invokes some determining principle which is extra physical (but not extra natural) to determine which of the two paths it is to follow.

When it is on the enveloping path it may at any instant, at its own sweet will, without exerting any force or spending any energy, go off along that one of the particular paths which happens to coincide with the actual condition of the system at that instant.

I think Boussinesq's method is a very powerful one against metaphysical arguments about cause and effect

It is extremely unlikely that Eddington believed that "free electrons" had the same kind of freedom he wanted for human beings, but he did speak loosely of the uncertainty associated with the electron breaking the hold on physical determinism. But his critics, especially L. Susan Stebbing accused Eddington of this. She said

"There is no way of discovering when an electron will jump, nor to which orbit it will jump. The initial state does not determine the final state; hence, the final state is unpredictable. It is unfortunate that this unpredictability has often been expressed by saying that the electron is 'free to choose' where it will jump. Such language is wholly inappropriate and has led to much confusion in discussions concerning the bearing of recent developments in physics upon the problem of free will." (Philosophy and the Physicists, 1937, p.178)

Eddington himself was more cautious, but he did hint the some "speck of brain matter" might be subject to indetermininism.

"There is in a human being some portion of the brain, perhaps a mere speck of brain-matter, perhaps an extensive region, in which the physical effects of his volitions begin,." (The Philosophy of Physical Science, 1938, p.182)

"The indeterminacy recognised in modern quantum theory is only a partial step towards freeing our actions from deterministic control." (The Nature of the Physical World, 1928, 313)

"The revolution of theory which has expelled determinism from present-day physics has therefore the important consequence that it is no longer necessary to suppose that human actions are competely predetermined. Although the door of human freedom is opened, it is not flung wide open; only a chink of daylight appears." (New Pathways in Science, 1935, p.87)

"I would even say that in the present indeterministic theory of the physical universe we have reached something which a reasonable man might almost believe." (New Pathways in Science, 1935, p.91)

In his 1931 Terry Lectures at Yale and the 1935 book, The Freedom of Man, and again in the 1940 book The Human Meaning of Science, Arthur Holly Compton developed this idea of the amplifier and added a daemon that might control a shutter, stopping "bad" photons. He imagined that a similar scheme whereby "consciousness could select the desirable brain current."

Imagine a faint ray of light passing through a tiny hole, which then spreads by diffraction into a broad beam. In the path of this broad beam we may place two photoelectric cells, A and B, each connected with an amplifier. These will be made so sensitive that the entrance of a single photon, i.e., particle of light, into either cell is recorded. A shutter in the path of the light ray remains open long enough to transmit a single photon. Into which cell will the photon fall ?

There is no way in which we can be sure. We have found that light has the dual aspect of waves and particles. The photon (particle) follows the light wave, and if we try to make its path more definite by using a smaller hole to transmit the ray, we merely make the transmitted beam of waves more diffuse by diffraction. Though the first photon may enter one cell, with the initial conditions identical as far as any test can show, the next photon may enter the other cell. The result is thus not reproducible. It is, as far as we can see, truly a matter of chance. That is what we mean by saying that the law of causality does not hold: knowledge of the initial conditions does not enable us to predict what will happen, for with the same initial conditions we cannot consistently produce the same effect.

According to modern physics, we thus live in a world of chance.

We might connect one of our amplifiers with an electrical device which will explode a stick of dynamite, and the other amplifier with a switch which will open the circuit. Now what will happen when the shutter transmits a photon? If it enters one cell the dynamite will explode, and the apparatus will be blown to bits. If the photon enters the other cell, the switch will be pulled and the apparatus is no longer in danger. Both events are equally probable. Similarly any event which depends at some stage upon the outcome of a small-scale event is essentially unpredictable on the basis of previous history.

Compton's demon - a close relative of Maxwell's demon

A daemon controlling the shutter might be conscious of their qualities. The daemon controlling the shutter might consider a photon which would enter the photoelectric cell that would result in exploding the dynamite a "bad" photon, and one which would enter the cell where it would prevent the catastrophe a "good" photon. Being directly conscious, of these nonphysical characteristics which will determine their direction, the daemon may then close the shutter to all approaching "bad" photons until a "good" photon has passed through and saved the day. Has the daemon in this way contravened any physical laws?

The point is that the event under consideration is really an individual act, to which, since it can be performed but once, the laws of statistics do not apply. Whether the switch is opened or the dynamite exploded by the first photon, in either case the experiment is complete. This corresponds closely to human action, considered in the light of habit. An experiment involving deliberation can be performed on a person only once; for afterwards his condition is not the same. Habit will now enter into the determination of his action. Thus deliberate actions likewise are individual events, and are not therefore predictable from laws of probability. Faced by the necessity for an individual decision, all one's physiological structure, his environment, and previous history determine what Warren Weaver describes as a "spectrum of action probability," within which "spectrum" it is possible for any action to be chosen. There will be greater probability for certain modes of action than others; but these probabilities do not specify the choice of the individual act.

It would be easy to outline a closely parallel scheme whereby consciousness could select the desirable brain current, even though the undesirable one might be equally probable from statistical considerations, thus leading to the performance of the desirable act rather than its alternative. It is not necessary to elaborate any particular brain mechanism for performing the selection, for the example just given shows that it is possible to select one of a number of physically possible acts without violating or modifying any physical law. In this way the determination of a man's actions by his will is, I believe, shown to be consistent with the principles of physics is they are now understood.

Eccles had as early as 1953 used Eddington's estimates of the uncertainty in neuron-sized structures to explore the possible interaction between a mental substance and brain matter. He made calculations of how far and fast a small unpredictable disturbance might radiate outward in a simplified model of a neural network.

The Neurophysiological Problem of Will

An important neurophysiological problem arises as soon as we attempt to consider in detail the events that would occur in the cerebral cortex when, by exercise of "will," some change is induced in the response to a given situation. As argued above, in a situation where "will" is operative, there will be a changed pattern of discharge down the pyramidal tract and this change must be brought about because there is a change in the spatio-temporal pattern of influences playing upon the pyramidal cells in the motor cortex. If the "will" really can modify our reactions in a given situation, we have somewhere in the complex patterned behaviour of the cortex to find that the spatiotemporal pattern which is evolving in that given situation is modified or deflected into some different pattern.

Quantitative Aspect of Spread of Activity in Neuronal Networks

In the formulation of problems concerning activity in neuronal network: it is of value to have a model of the simplest possible network (Fig. 28 A cf. BURNS, 1951, Fig. 10). Each neurone is assumed to have only two excitatory synaptic knobs on its surface and its axon has only two excitatory knobs on two other neurones. Further it is assumed that the synaptic connexions so formed are of a two-dimensional pattern that allows the neurones to be arranged schematically in the rectangular net-like form of Fig. 28A, where it will be noticed that there is virtual radial symmetry from any point and the possibility of indefinite extension in every direction.

If each neurone receives and gives three synaptic contacts, a similar construction with radial symmetry is possible in three-dimensional network (Fig. 28 B). As shown in Fig. 28 these constructions would give alternating direction of transmission in the successive lines in any plane. Similarly, if each neurone gave and received n synapses, the pattern could be accommodated to an n-dimensional network. The problem of the mode of action of the will can be simplified and sharpened by considering firstly the behavior of a single neurone in the active neuronal network of the cortex. Suppose some small "influence" were exerted at a node that would make a neurone discharge an impulse at a level of synaptic excitation which would otherwise have been just ineffective, that is, in general to raise the probability of its discharge. Such a discharged impulse would in turn have an excitatory effect on all the other nodes on which it impinges, raising the probability of their discharge, and so on. If we assume, as above, that the transmission time from node to node occupies 1 msec, then, even on the two-dimensional net of Fig. 28 A, a spread to a large number of neurones is possible in, say, 20 msec, a time that is chosen because it is at the lower limit of duration of discrete mental events.

In order to frame a precise problem, we can firstly consider the schematic neuronal networks of Fig. 28 which are assumed to be cortical neurones — both the pyramidal cells and the very numerous stellate cells. We make the postulates that at zero time a neurone (for example X in Fig. 28 A) is caused to discharge an impulse into the quiescent network and that activation of one synapse is adequate to cause any neurone to discharge an impulse. For the network of Fig. 28 A. the total number of neurones, N, caused to discharge impulses is given by the formula (SAWYER, 1951):

N = 2m² — 2m + 2

where m is the number of nodes traversed. In 20 msec m=20, the internodal time being assumed as 1 msec; hence the number of neurones activated is 762.

On the same assumptions, but with a multi-dimensional network constructed according to the conventions of Fig. 28, the number of activated neurones, N, is given, where m is large relative to n, by the general formula (SAWYER, 1951):

N ≈ (2n/n!) m²

when m = 20 (i. e. within 20 msec) and with n = 3 (Fig. 28 B), N is of the order 104. With n = 4 and 5 respectively, N is of the order 105 and 8 x 10⁵.

These calculations are intended merely to give some indication of the large number of cortical neurones that could be affected by a discharge originating in any one. In order to apply them to our problem of how "will" could act on the cerebral cortex, it is necessary to take into account the evidence that "will" can act on the cortical neuronal network only when a considerable part of it is at a relatively high level of excitation, i.e. we have to assume that, for "will" to be operative, large population, of cortical neurones are subjected to strong synaptic bombardment, and are stimulated thereby to discharge impulses which bombard other neurones. Under such dynamic conditions it may be conservatively estimated that, out of the hundred or more synaptic contacts made by any one neurone, at least four or five would be critically effective (when summed with synaptic bombardments by other neurones) in evoking the discharge of neurones next in series. The remainder would be ineffective because the recipient neurones would not be poised at this critical level of excitability, being either at a too low level of excitation, or at a too high level, so that the neuronal discharge occurs regardless of this additional synaptic bombardment. Thus at any instant the postulated action of the "will" on any one neurone would be effectively detected by the "critically poised neurones" on which it acts synaptically.

So long as the assumed number of critically effective synaptic excitatory actions by each neurone is kept at the low levels used in the above calculations, it is probable that the conventions of the network structures of Fig. 28 give an approximate method of allowing for all the mass of feed-back connections that occur in the closed-chain linkages of the cerebral cortex (LORENTE DE NO, 1933, 1934, 1943). Further, since the cortex is approximately 3 mm thick and the mean density of neurones 40,000 per sq. mm of surface (THOMPSON, 1899), the spread to some hundreds of thousands of neurones can be treated as spreading indefinitely in all directions without serious restriction by the sheet-like structure of the cortex. Hence we may conclude that, when a region of the cortical neuronal network is at a high level of activity, the discharge of an impulse by any one neurone will have contributed directly and indirectly to the excitation of hundreds of thousands of other neurones within the very brief time of 20 msec.

A Neurophysiological Hypothesis of Will

As a restatement of the conclusion of the preceding section we may say that in the active cerebral cortex within 20 msec the pattern of discharge of even hundreds of thousands of neurones would be modified as a result of an "influence " that initially caused the discharge of merely one neurone. But further, if we assume that this "influence" is exerted not only at one node of the active network, but also over the whole field of nodes in some sort of spatio-temporal patterning, then it will be evident that potentially the network is capable of integrating the whole aggregate of "influences" to bring about some modification of its patterned activity, that otherwise would be determined by the pattern of afferent input and its own inherent structural and functional properties. Such integration would occur over hundreds of thousands of nodes in a few milliseconds, the effects exerted on any and every node being correlated in the resultant patterned activity of the surrounding hundreds of thousands of neurones. Thus in general. the spatio-temporal pattern of activity would be determined not only by (i) the micro-structure of the neural net and its functional properties as built up by genetic and conditioning factors and (ii) the afferent input over the period of short-term memory, but also (iii) by the postulated "field of mind influence." For example, in Fig. 29 the spatio-temporal pattern determined by factors (i) and (ii) is shown diagrammatically by the shaded structure bounded by the continuous line, while a possible modification by factor (iii) is indicated by the paths outlined by broken lines at B and C. Fig. 29 can be considered as showing boundaries of multilane neuronal traffic as indicated in Figs. 10 and 12.

It can be claimed that no physical instrument would bear comparison with the postulated performance of the active cerebral cortex as a detector of minute "fields of influence" spread over a microscopic pattern am with temporal sequences of milliseconds. The integration, within a few milliseconds, of "influences" picked up at hundreds of thousands of nodes would be unique, particularly when it is remembered that the integration is no mere addition, but is exerted to modify in some specific way "a shifting harmony of sub-patterns" of neuronal activity, achieving expression through the modifications so produced.

Thus, the neurophysiological hypothesis is that the "will" modifies the spatiotemporal activity of the neuronal network by exerting spatiotemporal "fields of influence" that become effective through this unique detector function of the active cerebral cortex. It will be noted that this hypothesis assumes that the "will" or "mind influence" has itself some spatio-temporal patterned character in order to allow it this operative effectiveness.

While the Gomes model is little more than an elaboration of Arthur Holly Compton's amplifier, it is at least more peaceful. Where Compton's photocell amplifiers blow up dynamite, Gomes' multiple electron detectors and computer algorithms play music on a piano.

A MERELY PHYSICAL ILLUSTRATION

In truth, if a machine is steered by a complex interlocking of several units of indeterminate and determinate control, the number of states it can come to under the determining influence of the overall controlling situations of the steerage system can be as large, in principle, as the number of the combinations among the differentiated indeterminate configurations possible for each unit of indeterminate control. Yet, while planning the system, we can easily do it in such a way that only the controlling situations which can be interpreted as orderly are allowed to work out their influence. But the selection among these would still be indeterminate, because dependent on physically uncertain processes. This principle can be true both of the final situations of the machine considered statically, and of the successions among them — which means that these successions themselves can also be made at the same time well ordered and indeterminate.

It would be convenient to introduce a concrete illustration of a case of this nature. To this effect, let us imagine, as a unit of indeterminate control, a cylindrical vacuum chamber with a very tiny aperture in the center of one of its transversal walls, and a ring with a certain number of differentiated parts electrically insulated from one another and each of them connected to a high-sensitivity detector amplifier capable of responding to discrete manifestations of electrons of very low energy over the corresponding area of the ring. Let its also suppose a source of low-energy electrons before the aperture in the first wall, and a low accelerating difference of potential between the two ends of the chamber. If the aperture is small enough, each electron which penetrates the chamber will have its spatial localization very sharply defined, and will consequently suffer a physically indeterminate disturbance of momentum, with the magnitude given by the uncertainty relations of Heisenberg. The chamber can be so constructed that the medium diameter of the ring in the second transversal wall coincides with the region of the most probable manifestation of the indeterminately disturbed electrons. The place where each electron will appear upon this ring — and thus upon one or other of its several differentiated parts — is completely indeterminated, and the laws of microphysics require only that in sets of relatively large numbers of individual manifestations their distribution be uniform along the circumference of the ring, and thus that the number of the discrete arrivals upon each part of it be approximately equal for all of them. There is, however, absolutely no law for the localization of a particular manifestation upon the ring or for the step-to-step successions.

An orderly but physically indeterminate machine. Compare Compton's photocell amplifiers.

If we connect some macrophysical gadget to each of the detector amplifiers coupled to the several elements of the ring, and have those gadgets performing some macrophysical operation under the switch-on, switch-off command of the detector amplifiers, in such a way that they are put to work or to rest every time that a disturbed electron manifests itself upon the corresponding part of the ring, the assembly as a whole will constitute a macrophysical system completely undetermined in the order of its final operations. We can imagine, for instance, a jukebox with the selection of its records commanded by a unit of indeterminate control, or some sort of roulette under the same guidance.

So far, our device illustrates only physical indetermination in a series of macrophysical processes which can be in themselves either very simple — the case of the roulette — or very elaborate — the case of the reproduction of a record in the jukebox. With the further purpose of illustrating order which is significantly indeterminate all along its development, let us now imagine a piano Fig. 18.1 with a certain number of keys — say, 100 — and the activation of each of these keys decided by the output of one indeterminate control with a corresponding number of possible different states. Let the connection between this device of indeterminate control and the final mechanism of activation of the keys pass through circuitry specially designed to switch it off every time that the message started a unit that does not conform to a set of rules of musical composition which can be translated into the intermediary circuitry. This circuitry may, of course, incorporate a recording mechanism for all the operations of the system; and the rules of composition may accordingly state that after the successful activation of one key of the piano, only a few other keys — say, 5 among the 100 — may follow. The rules may also be such that in certain special cases they condition the activation of a new key in a sequence, not only to the immediately preceding element, but also to whole previous passages of the sequence; and they may as well comprehend other factors of musical composition such as rhythm and harmony of simultaneously sounding notes. Yet, as long as each new step in the musical succession admits more than one possibility which is in turn decided by the indeterminate control, the output of the instrument will also remain undetermined, irrespectively of the high degree of order and organization which it can maintain.

Now, if elaborate and ordered, but physically uncertain and, in not very long runs, statistically irregular work is thus possible for merely physical machines, it is clearly also possible, in principle, for living beings — very specially for those with a highly developed nervous system. Such a nervous system may house millions or billions of nearly simultaneous processes equivalent to those described in connection with a unit of indeterminate control, and have all these connected according to the most elaborate interlocking; hence it can afford the opportunity for the accomplishment of sequences of meaningful, organized, and not-statistically monotonous behavior, very far exceeding in length of time the span of individual life.

Dennett

Kane

Ekstrom

Mele